One end of a long string of linear mass dnesity `8.0xx10^(-3)kgm^(-1)` is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At `t=0` the left end (fork end) of the string `x=0` has zero transverse displacement `(y=0)` and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describest the wave on the string.

Explanation

M = `8.0 xx 10^(-3) kg m^(-1)`, Amplitude, A = 5 cm = 0.05 m, v = 256 Hz
`upsilon = sqrt((T)/(M)) = sqrt((mg)/(M))`
`= sqrt((90 xx 9.8)/(8.0 xx 10^(-3))) = 3.32 xx 10^(2) ms^(-1)`
So `omega = 2 pi v = 2 xx 3.142 xx 3.32 xx 10^(2)`
`= 1.61 xx 10^(3) s^(-1)`
And `lambda = (upsilon)/(v) = (3.32 xx 10^(2))/(256) = 1.29`
`k = (2pi)/(lambda) = 4.86 m^(-1)`
The equation of the wave is
`y = 0.05 sin (omega t - kx)`
putting the values we get `y = 0.05 sin (1.61 xx 10^(3) t - 4.86 x)`
where x and y are in m.